Question

From a well-shuffled pack of $52$ cards, three kings and two black jacks are removed. From the remaining cards, a card is drawn at random. Find the probability that the card drawn is neither an ace nor a king.

Answer 1

Step 1 Finding the number of favorable and total number of outcomes:

Given that there is a well-shuffled pack of $52$ cards.

Since three kings and two black jacks are removed,

$52-3-2=47$

So, the total number of outcomes will be $47$.

In a pack of $52$ cards, there are $26$ red cards and $26$ black cards.

There are four suits - Heart, Diamond, Club and Spade having $13$ cards each.

There are four face cards - ace, king, queen and jack in each suit.

So, the number of cards that are neither ace nor kings would be

$$\begin{gathered} Remainingcards-acecards-1kingcard \\ \Rightarrow 47-4-1 \\ \Rightarrow 42 \end{gathered}$$

So, the number of favorable outcomes is $42$.

Step 2 Finding the probability of drawing a card that is neither an ace nor a king:

The formula for probability is

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

$\therefore P(neitheranacenoraking)=\frac{42}{47}$

Hence, the probability of drawing a card that is neither an ace nor a king is $\frac{42}{47}$.